You have two W7s? That is ridiculous for the LS.
Anyways there is no such thing as underpowering woofers and it damaging an amplifier (or the driver(s) for that matter).
Big 3 and two batteries is a good start, but the LS's stock alternator is built for what seems to be just enough amperage for the allotted accessories. Judging by your screenname, it appears you have a first generation LS - in which the alternator is 110amp unless I am mistaken. (second gen is 140amp, just for reference).
If you have ditched the hydraulic cooling fan, you are also using up some of the wiggle room in amperes.
I believe the first generation LS does have a high output alternator option that is decently reliable.
My suggestion is either look into the HO alternator, or drop a woofer and run a <1000k watt amp. With the money spent on amplifiers, you may as well get yourself the alt since it appears you cannot turn down the volume when the engine is running low RPMs.